Motion analyzing apparatus

ABSTRACT

A sensor unit is installed to a target object and detects a given physical amount. A data acquisition unit acquires output data of the sensor unit in a period including a first period for which a real value of a value of m time integrals of the physical amount is known and a second period that is a target for motion analysis. An error time function estimating unit performs m time integrals of the output data of the sensor unit and estimates a time function of an error of a value of the physical amount detected by the sensor unit with respect to the real value of the value of the physical amount detected by the sensor unit based on a difference between a value of m time integrals of the output data and the real value for the first period.

BACKGROUND

1. Technical Field

The present invention relates to a motion analyzing apparatus.

2. Related Art

In various fields, apparatuses that analyze the motion of a person or anobject are necessary. For example, by analyzing the swing trajectory ofa tennis racket or a golf club, the form of baseball pitching orbatting, and the like and clarifying points to be improved based on theanalysis result, game power can be improved.

Currently, as practical motion analyzing apparatuses, apparatuses thatanalyze a motion by consecutively photographing a measurement object, towhich a mark is attached, using an infrared camera or the like andcalculating the motion trajectory of the mark using consecutivephotographed images are generally used.

JP-A-2004-24488 is an example of the related art.

However, in such apparatuses, since an infrared camera used forphotographing images is necessary, the size of the apparatuses is inconsequence large, and, accordingly, there is a problem in that it isdifficult to handle the apparatuses. For example, in a case where theimages of a tennis practice are desired to be acquired throughphotographing at a plurality of angles, it is necessary to move theposition of the infrared camera or change the direction of a player inaccordance with the desired photographing angles.

In contrast to this, recently, an apparatus was proposed which analyzesthe motion of a measurement object based on output data of a smallinertial sensor by installing the inertial sensor in the measurementobject. Such an apparatus does not need an infrared camera, andaccordingly there is an advantage of easy handling. For example, thevelocity v(t) and the position p(t) of the measurement object can becalculated by performing a time integration process as shown in thefollowing Equations (1) and (2) for an acceleration value a(t) detectedby an acceleration sensor.

v ⁡ ( T ) = ⁢ a ⁡ ( t ) ⁢ ⅆ t + v 0 ( 1 ) p ⁡ ( T ) = ∫ 0 T ⁢ v ⁡ ( t ) ⁢ ⅆ t +p 0 = ∫ 0 T ⁢ ∫ 0 T ⁢ a ⁡ ( τ ) ⁢ ⅆ τ ⁢ ⅆ t + v 0 ⁢ T + p 0 ( 2 )

However, generally, an error other than a value to be observed isincluded in the output value of an inertial sensor. Accordingly, forexample, the output data x(t) of the acceleration sensor can berepresented as the following Equation (3) by using an acceleration valuea(t) and an error ε(t).x(t)=a(t)+ε(t)  (3)

Accordingly, in a case where the velocity v(t) and the position p(t) ofa measurement object are calculated by performing a time integrationprocess as represented in the following Equations (4) and (5) based onthe output data x(t) of the acceleration sensor, the error ε(t) isintegrated with respect to time as well. Therefore errors in thevelocity v(t) and the position p(t) rapidly increase in accordance withthe elapse of time t.

$\begin{matrix}{{\int_{0}^{t}{{x(t)}\ {\mathbb{d}t}}} = {{v(T)} + {\int_{0}^{\tau}{{ɛ(t)}\ {\mathbb{d}t}}} + c_{1}}} & (4) \\{{\int_{0}^{\tau}{\int_{0}^{t}{{x(\tau)}{\mathbb{d}\tau}\ {\mathbb{d}t}}}} = {{p(T)} + {\int_{0}^{\tau}{\int_{0}^{t}{{ɛ(\tau)}\ {\mathbb{d}\tau}{\mathbb{d}t}}}} + {c_{1}T} + c_{2}}} & (5)\end{matrix}$

In other words, in a motion analyzing apparatus using an inertialsensor, the characteristics of the sensor are not sufficient inpractice, and in a case where the posture, the velocity, the position,and the like are calculated by performing an integration process for theoutput data of the inertial sensor, an error included in the output ofthe sensor noticeably increases through the integration process, wherebythere is problem in that a sufficient analysis (measurement) capabilityis not acquired.

SUMMARY

An advantage of some aspects of the invention is that it provides amotion analyzing apparatus that can be easily handled and provideanalysis information with sufficient accuracy.

(1) An aspect of the invention is directed to a motion analyzingapparatus including: a sensor unit that is installed to a target objectand detects a physical amount; a data acquisition unit that acquiresoutput data of the sensor unit in a period including a first period forwhich a real value of a value of m time integrals (here, m is an integerequal to or greater than one) of the physical amount is known and asecond period that is a target for motion analysis; an error timefunction estimating unit that performs m time integrals of the outputdata and estimates a time function of an error of a value of thephysical amount detected by the sensor unit with respect to the realvalue based on a difference between a value of m time integrals of theoutput data and the real value for the first period; a data correctingunit that corrects a value of m time integrals of the output data forthe second period based on an estimation result of the error timefunction estimating unit; and a motion analysis information generatingunit that generates motion analysis information of the target objectbased on the value of the m time integrals for the second period that iscorrected by the data correcting unit.

The target object to be analyzed may be a person or an object (forexample, an exercise tool, a vehicle, or the like) other than a person.

The information used for analyzing the motion of a target object, forexample, may be trajectory information of the target object orinformation of a change in the speed of the target object, or the like.

The m time integrals may be an m time integrals in a continuous timesystem or an m time integrals (m time differentials) in a discrete timesystem.

According to the above-described motion analyzing apparatus, thedetection error of the sensor unit is estimated as a time function, andthe m time integrals of the physical amount of the detection target iscorrected by using the estimated time function of the error, wherebyanalysis information having sufficient accuracy can be generated. Inaddition, a sensor is used instead of an infrared camera, theconfiguration can be simplified, and the handling thereof is easy.

(2) In the above-described motion analyzing apparatus, the error timefunction estimating unit may estimate the time function of the error byapproximating the time function of the error as a polynomial equationand calculating coefficients of the polynomial equation.

In such a case, the time function of the detected error can be estimatedwith sufficient accuracy through relatively simple calculation. Inaddition, the order of the polynomial may be determined based on theaccuracy required for the motion analysis.

In addition, for example, the error time function estimating unit maycalculate coefficients of the polynomial equation by solvingover-determined simultaneous equations that are acquired byapproximating the error of the m time integrals of the data acquired bythe data acquisition unit for the first period with respect to the realvalue to the value of the m time integrals of the polynomial in thefirst period of the polynomial equation.

As above, by setting up the over-determined simultaneous equations byacquiring more data in the first period, the estimation accuracy of thetime function of the detected error can be increased. In addition, forexample, the over-determined simultaneous equations may be solved byusing a least squares method.

(3) The above-described motion analyzing apparatus may be configuredsuch that a plurality of the first periods is set, and the error timefunction estimating unit estimates the time function of the error basedon data for each of the plurality of the first periods that is acquiredby the data acquiring unit.

By arranging a plurality of the first periods as above, the estimationaccuracy of the time function of the detected error can be increasedfurther.

(4) The above-described motion analyzing apparatus may be configuredsuch that at least one of the plurality of the first periods is a periodbefore start of the second period, and at least one of the plurality ofthe first periods is a period after end of the second period.

In such a case, the estimation accuracy of the time function of thedetected error for the second period as a target of the motion analysiscan be further increased, and accordingly, the motion analysisinformation having higher accuracy can be generated.

(5) In the above-described motion analyzing apparatus, the first periodmay be a period in which the target object is stopped.

In such a case, for example, the speed, the posture, and the position ofthe target object for the first period can be known.

(6) In the above-described motion analyzing apparatus, the sensor unitmay detect at least one of acceleration and angular velocity as thephysical amount.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a diagram showing the configuration of a motion analyzingapparatus according to this embodiment.

FIG. 2 is a flowchart showing an example of a process of generatingmotion analysis information by using a processing unit.

FIGS. 3A and 3B are diagrams showing examples of a data acquisitionperiod, a first period, and a second period.

FIG. 4 is a flowchart illustrating a process of estimating an error timefunction and a data correcting process.

FIG. 5 is a schematic diagram showing the configuration of a sensor unitin this experimental example.

FIG. 6 is a diagram showing an example of installation of the sensorunit in this experimental example.

FIG. 7 is a diagram illustrating the operation sequence of a testsubject in this experimental example.

FIG. 8 is a diagram illustrating the definition of a coordinate systemin this experimental example.

FIG. 9 is a flowchart showing the process performed by a processing unitin this experimental example.

FIGS. 10A and 10B are diagrams showing trajectory data in thisexperimental example.

FIGS. 11A and 11B are diagrams for comparing trajectory data accordingto a technique of this embodiment and trajectory data according to ageneral technique.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, a preferred embodiment of the invention will be describedin detail with reference to the accompanying drawings. The embodimentdescribed here is not for purposes of inappropriately limiting thecontent of the invention that is defined in the claims. In addition, notall the configurations described below are determined as essentialconstituent elements of the invention.

FIG. 1 is a diagram showing the configuration of a motion analyzingapparatus according to this embodiment.

The motion analyzing apparatus 1 according to this embodiment isconfigured so as to include one or a plurality of sensor units 10 and ahost terminal 20 and analyzes the motion of a target object. The sensorunit 10 and the host terminal 20 are interconnected in a wired orwireless manner.

The sensor unit 10 is installed to a target object for motion analysisand performs a process of detecting a given physical amount. In thisembodiment, the sensor unit 10 is configured so as to include one or aplurality of sensors 100, a data processing section 110, and acommunication section 120.

The sensor 100 is a sensor that detects a given physical amount andoutputs a signal (data) according to the magnitude of the detectedphysical amount (for example, acceleration, angular velocity, speed,angular acceleration, or the like). For example, the sensor 100 is aninertial sensor.

The data processing section 110 synchronizes output data of each sensor100, forms a packet in which the data is combined with time informationand the like, and outputs the packet to the communication section 120.In addition, the data processing section 110 may perform the process ofcorrecting the bias of the sensor 100 and correcting the temperature.Alternatively, the function of bias correction and temperaturecorrection may be introduced into the sensor 100.

The communication section 120 performs the process of transmitting thepacket data received from the data processing section 110 to the hostterminal 20.

The host terminal 20 is configured so as to include a processing unit(CPU) 200, a communication unit 210, an operation unit 220, a ROM 230, aRAM 240, a non-volatile memory 250, and a display unit 260.

The communication unit 210 performs the process of receiving datatransmitted from the sensor unit 10 and transmitting the data to theprocessing unit 200.

The operation unit 220 performs the process of acquiring operation datafrom a user and transmitting the operation data to the processing unit200. The operation unit 220, for example, is a touch panel-type display,buttons, keys, a microphone, or the like.

The ROM 230 stores programs used for performing various calculationprocesses and control processes of the processing unit 200, variousprograms and data for implementing application functions, and the like.

The RAM 240 is used as a work area of the processing unit 200 and is astorage unit that temporarily stores a program or data read out from theROM 230, data input from the operation unit 220, calculation results ofthe processing unit 200 that are acquired through execution of variousprograms, and the like.

The non-volatile memory 250 is a recording unit that records data whichneeds to be stored for a long term out of data generated by the processof the processing unit 200.

The display unit 260 displays the processing result of the processingunit 200 as a text, a graph, or other images. The display unit 260, forexample, is a CRT, an LCD, a touch panel-type display, an HMD (headmount display), or the like. In addition, the functions of the operationunit 220 and the display unit 260 may be realized by one touchpanel-type display.

The processing unit 200 performs various calculation processes for datareceived from the sensor unit 10 through the communication unit 210 orvarious control processes (display control for the display unit 260 orthe like) in accordance with programs stored in the ROM 240.

Particularly, in this embodiment, the processing unit 200 serves as adata acquisition section 202, an error time function estimating section204, a data correcting section 206, and a motion analysis informationgenerating section 208 to be described later.

The data acquisition section 202 performs the process of acquiringoutput data of the sensor unit 10 in a period including a first periodin which the real value of the value of m time integrals of the physicalamount as a detection target of the sensor 100 is known and a secondperiod as a motion analysis target. The acquired data, for example, isstored in the RAM 240.

The error time function estimating section 204 calculates m integrals ofthe output data of the sensor unit and performs the process ofestimating a function (hereinafter, referred to as an “error timefunction) of an error with respect to the real value of the value of thephysical amount detected by the sensor unit 10 in time based on adifference between the value of the m time integrals of the output datafor the first period and the real value.

The data correcting section 206 performs the process of correcting thevalue of the m time integrals of the output data of the sensor unit 10for the second period based on the estimation result of the error timefunction estimating section 204.

The motion analysis information generating section 208 performs theprocess of generating information used for analyzing the motion of atarget object (hereinafter, referred to as “motion analysisinformation”) based on the value of the m time integrals for the secondperiod that has been corrected by the data correcting section 206. Thegenerated motion analysis information may be displayed as a text, agraph, a diagram, or the like on the display unit 260 or may be outputto the outside of the host terminal 20.

FIG. 2 is a flowchart showing an example of the process of generatingmotion analysis information by using the processing unit 200.

First, the processing unit 200 periodically acquires new data from thesensor unit 10 until a data acquisition period ends (No in Step S20) byusing the data acquisition section 202 (Step S10).

Next, when the data acquisition period ends (Yes in Step S20), theprocessing unit 200 calculates m time integrals of the data (Step S21)in the first period and estimates the error time function based on adifference between the m time integrals of the data acquired in Step S10and the real value, by using the error time function estimating section204 (Step S30).

Next, the processing unit 200 corrects the value of the m time integralsof the data acquired in Step S10 for the second period based on the timefunction estimated in Step S30, by using the data correcting section 206(Step S40).

Finally, the processing unit 200 generates motion analysis informationbased on the value of the m integrals for the second period with respectto time, which has been corrected in Step S40, by using the motionanalysis information generating section 208 (Step S50).

FIGS. 3A and 3B are diagrams showing examples of the data acquisitionperiod, the first period, and the second period.

In the example shown in FIG. 3A, a second period for which an analysistarget object moves is arranged at time t2 to t3, and, before and afterthe second period, two first periods that are separated in time arearranged at t0 to t1 and t4 to t5. In addition, a data acquisitionperiod is arranged at time t0 to t5, for this data acquisition period,the output data of the sensor unit 10 is sampled (acquired) at apredetermined interval by the host terminal 20. In each of the two firstperiods, since the real value of m time integrals of the physical amountas the detection target of the sensor unit 10 is known, a differencebetween the value of m time integrals of the output data of the sensorunit 10 and the real value can be known. An error time function for theoutput data of the sensor unit 10 can be estimated for the entire dataacquisition period based on the information of the difference. Inaddition, any one of the first period (time t0 to t1) that is arrangedfirst and the first period (time t4 to t5) arranged second may not beprovided. However, in order to increase the accuracy of the estimationof the error time function, it is preferable that the first periods arearranged before and after the second period. In order to increase theaccuracy of estimation of the error time function, it is effective toestimate the error time function by reflecting random variations of theerror that is caused by the variations of the power source, temperaturevariations, and the like, accordingly, it is preferable that a pluralityof the first periods that are separated in time are arranged.Particularly, by arranging the first periods before and after the secondperiod, the accuracy of the estimated error increases for the secondperiod, and accordingly, the accuracy of data correction for the secondperiod can be improved.

In addition, in the example shown in FIG. 3B, two second periods inwhich the analysis target object moves are arranged at time t2 and t3and time t4 and t5. The first period (time t3 to t4) is arranged beforethe second period (time t2 to t3) arranged first, the first period (timet3 to t4) arranged second is arranged between the two second periods,and the first period (time t6 to t7) arranged third is arranged afterthe second period arranged second. Then, the data acquisition period isarranged at time t0 to t7. For each one of the three first periods, thereal value of m integrals of the physical amount as the detection targetof the sensor unit 10 is known, a differences between the value of mtime integrals of the output data of the sensor unit 10 and a real valuecan be known. The error time function for the output data of the sensorunit 10 can be estimated for the entire data acquisition period. Inaddition, in the example shown in FIG. 3B, since two second periods astargets of motion analysis are arranged, by arranging three firstperiods at positions that are separated in time with the two secondperiods interposed therebetween, the estimation accuracy of the errortime function for the two second periods can be increased. In otherwords, by arranging the first periods before and after the second periodas targets of motion analysis, even in a case where motions of theanalysis targets are repeatedly performed over time, the correctionaccuracy of the data for each second period can be improved.

Estimation of Error Time Function and Data Correction

Next, an example of the technique for estimating the error time functionand data correction will be described.

First, in a case where the value of the physical amount as a calculationtarget of the processing unit 200 at time t is assumed to be F_(m)(t),and the sensor unit 10 measures the value f(t) of the m-th orderderivative function, the following Equation (6) is satisfied.

$\begin{matrix}{\frac{\mathbb{d}^{m}{F_{m}(t)}}{\mathbb{d}t^{m}} = {f(t)}} & (6)\end{matrix}$

Here, assuming that the output data x(t) of the sensor unit 10 includesan error ε(t), x(t) can be represented as the following Equation (7).x(t)=f(t)+ε(t)  (7)

It can be considered that the error time function ε(t) is approximatedas an n-th order polynomial equation ε(t) as the following Equation (8).

$\begin{matrix}{{{ɛ(t)} \approx {g(t)}} = {{a_{0} + {a_{1}t} + {a_{2}t^{2}} + \ldots + {a_{n}t^{n}}} = {\sum\limits_{k = 0}^{n}{a_{k}t^{k}}}}} & (8)\end{matrix}$

In X_(m)(t) that is the result of m time integrals of the output datax(t) of the sensor unit 10, an error component E_(m)(t) due to aninitial state error ε(t) (integral constant) other than the physicalamount F_(m)(t) as a calculation target is included. Accordingly,X_(m)(t) can be represented as the following Equation (9).

$\begin{matrix}{{{X_{m}(t)} = {{F_{m}(t)} + {E_{m}(t)}}}\left\{ \begin{matrix}{\frac{\mathbb{d}^{m}{X_{m}(t)}}{\mathbb{d}t^{m}} = {x(t)}} \\{\frac{\mathbb{d}^{m}{E_{m}(t)}}{\mathbb{d}t^{m}} = {ɛ(t)}}\end{matrix} \right.} & (9)\end{matrix}$

Considering that the error component E_(m)(t) can be approximated as apolynomial equation G_(m)(t) in consideration of the integral constant(initial state error) c_(K) for the m time integrals of g(t), thefollowing Equations (10) and (11) are satisfied.

$\begin{matrix}{\frac{\mathbb{d}^{m}{G_{m}(t)}}{\mathbb{d}t^{m}} = {g(t)}} & (10) \\{{{E_{m}(t)} \approx {G_{m}(t)}} = {{\sum\limits_{k = 0}^{n}{\frac{k!}{\left( {k + m} \right)!}a_{k}t^{k + m}}} + {\sum\limits_{k = 0}^{m - 1}{\frac{c_{m - k}}{k!}t^{k}}}}} & (11)\end{matrix}$

Accordingly, in a case where the physical amount F_(m)(t_(r)) atspecific time t_(r) is known, the relation represented in the followingEquation (12) is satisfied.

$\begin{matrix}{{{{X_{m}\left( t_{r} \right)} - {F_{m}\left( t_{r} \right)}} \approx {G_{m}\left( t_{r} \right)}} = {{\sum\limits_{k = 0}^{n}{\frac{k!}{\left( {k + m} \right)!}a_{k}t_{r}^{k + m}}} + {\sum\limits_{k = 0}^{m - 1}{\frac{c_{m - k}}{k!}t_{r}^{k}}}}} & (12)\end{matrix}$

By preparing this relation equations of Equation (12) corresponding tothe number of each time at which the value of the physical amount as acalculation target is known, for coefficients a_(K) and C_(K) ofEquation (11) as an approximated polynomial equation, the followingEquation (13) as over-determined simultaneous equations as below can beset up.

$\begin{matrix}{{\begin{bmatrix}{{X_{m}\left( t_{r\; 1} \right)} - {F_{m}\left( t_{r\; 1} \right)}} \\{{X_{m}\left( t_{r\; 2} \right)} - {F_{m}\left( t_{r\; 2} \right)}} \\{{X_{m}\left( t_{r\; 3} \right)} - {F_{m}\left( t_{r\; 3} \right)}} \\\vdots\end{bmatrix} \approx {{U\begin{bmatrix}a_{0} \\a_{1} \\\vdots \\a_{n}\end{bmatrix}} + {V\begin{bmatrix}c_{1} \\c_{2} \\\vdots \\c_{m}\end{bmatrix}}}}\left\{ \begin{matrix}{{U = \left\{ u_{ij} \right\}},} & {u_{ij} = {\frac{j!}{\left( {m + j} \right)!}t_{ri}^{m + j}}} \\{{V = \left\{ v_{ij} \right\}},} & {v_{ij} = {\frac{1}{\left( {m - j} \right)!}t_{ri}^{m - j}}}\end{matrix} \right.} & (13)\end{matrix}$

From Equation (13) as the over-determined simultaneous equations, thecoefficients a_(K) and C_(K) of Equation (11) as the approximatedpolynomial equations can be acquired, for example, by using aleast-squares method.

$\begin{matrix}{M = \begin{bmatrix}U & V\end{bmatrix}} & (14) \\{\begin{bmatrix}a_{0} \\a_{0} \\\vdots \\a_{n} \\c_{1} \\c_{2} \\\vdots \\c_{m}\end{bmatrix} = {\left( {M^{T}M} \right)^{- 1}{M^{T}\begin{bmatrix}{{X_{m}\left( t_{r\; 1} \right)} - {F_{m}\left( t_{r\; 1} \right)}} \\{{X_{m}\left( t_{r\; 2} \right)} - {F_{m}\left( t_{r\; 2} \right)}} \\{{X_{m}\left( t_{r\; 3} \right)} - {F_{m}\left( t_{r\; 3} \right)}} \\\vdots\end{bmatrix}}}} & (15)\end{matrix}$

Since the approximated polynomial equations g(t) and G_(m)(t) aredetermined by using the coefficients a_(K) and C_(K), the physicalamount F_(m)(t) and the value f(t) of the m-th order derivative functionthereof can be estimated by using the following Equations (16) and (17).F _(m)(t)≈X _(m)(t)−G _(m)(t)  (16)f(t)≈x(t)−g(t)  (17)

The flowchart of the error time function estimating process and the datacorrection process based on the above-described techniques areillustrated in FIG. 4.

First, the m time integrals of the acquired data x(t) is performed so asto calculate X_(m)(t) (Step S32).

Next, the error time function ε(t) is approximated as a polynomialequation g(t), and Equation (13) as the over-determined simultaneousequations is generated by using the value X_(m)(t_(r)) of the m timeintegrals at each time t_(r) in the first period and the real valueF_(m)(t_(r)) (Step S34).

Next, the Equation (13) as the over-determined simultaneous equationsgenerated in Step S34 is solved so as to calculated the coefficientvalues a_(K) and c_(K) of g(t) (Step S36).

Next, G_(m)(t) is calculated from Equation (11) by using the coefficientvalues a_(K) and c_(K) calculated in Step S36 (Step S38).

Finally, F_(m)(t) is calculated from Equation (16) by using X_(m)(t)calculated in Step S32 and G_(m)(t) calculated in Step S36 (Step S42).

Here, the process of Steps S32 to S38 corresponds to the process of StepS30 illustrated in the flowchart of FIG. 2, and the process of Step S42corresponds to the process of Step S40 illustrated in the flowchart ofFIG. 2.

As described above, according to the motion analyzing apparatus of thisembodiment, motion analysis information having sufficient accuracy canbe generated by estimating the error time function of the output data ofthe sensor unit 10 and correcting the value of the m time integrals ofthe output data of the sensor unit 10. In addition, according to thisembodiment, the sensor is used instead of the infrared camera, andaccordingly, a motion analyzing apparatus that has a simpleconfiguration and can be easily handled can be realized.

In addition, according to this embodiment, by approximating the errortime function as a polynomial equation, the error time function can beestimated with sufficient accuracy, for example, through relativelysimple calculation as Equation (15). In addition, by acquiring more datafor the first period and setting up Equation (13) as the over-determinedsimultaneous equations, the estimation accuracy of the error timefunction can be raised.

Experimental Example of Motion Analysis

Next, an experimental example will be described to which the motionanalyzing technique of this embodiment is applied. In this experimentalexample, the sensor unit 10 configured as shown in FIG. 5 is installedto a grip end of a tennis racket as an analysis target object as shownin FIG. 6, and the trajectories (an example of the motion analysisinformation) of the top 302 and the grip end 304 of the tennis racketwhen the test subject hits a tennis ball are represented.

As shown in FIG. 5, the sensor unit 10 used in this experimental exampleincludes a six-axis motion sensor that is configured by three axisacceleration sensors 102 x, 102 y, and 102 z (examples of inertialsensors) that detect the acceleration in the directions of the X axis,the Y axis, and the Z axis and three axis gyro sensors (angular velocitysensors) 104 x, 104 y, and 104 z that detect the angular velocities inthe directions of the X-axis, the Y-axis, and the Z-axis, as the sensor100 shown in FIG. 1. The X-axis, the Y-axis, and the Z-axis aredetermined based on the right-hand system.

The data processing section 110 synchronizes the output data of thesix-axis motion sensor and outputs the synchronized data to thecommunication section 120. In addition, the data processing section 110performs the process of correcting a detected error due to a deviationof the installation angle of the six-axis motion sensor and the like.

The communication section 120 performs the process of transmitting thedata received from the data processing section 110 to the host terminal20.

This sensor unit 10, for example, as shown in FIG. 6, is installed tothe grip end 304 of the tennis racket 300 such that the X axis isperpendicular to the face (hitting area). The installation direction ofthe sensor unit 10 is arbitrary. For example, as shown in FIG. 6, thesensor unit 10 is installed such that the x-axis direction is thedirection of a perpendicular line extending from the inside of the sheetface toward the front side, the y-axis direction extends toward theright side in the horizontal direction, and the z-axis direction extendstoward the upper side in the vertical direction.

In this experimental example, the test subject is allowed to perform apredetermined operation sequence. This operation sequence will bedescribed with reference to FIG. 7. First, the tennis racket 300 isplaced at a first position determined in advance and is stopped at leastabout one second (time t0 to t1). Next, the test subject moves to asecond position with the tennis racket 300 held and prepares a swing(time t1 to t2). Next, the tennis ball is sent to the test subject, andthe test subject hits the tennis ball with the tennis racket 300 (timet2 to t3). Next, after finishing the swing, the test subject moves tothe first position with the tennis racket held and places the tennisracket at the first position (time t3 to t4). Finally, the tennis racket300 is stopped for at least about one second (time t4 to t5). The periodof time t0 to t5 corresponds to the data acquisition period, and, theoutput data of the sensor unit 10 is sampled, for example, at thesampling rate (0.5 kHz) of 500 samples per second. In addition, in theperiod of time t0 to t1 and the period t4 to t5, the positions of thesensor unit 10 are known and the period corresponds to the first period.Furthermore, the period of time t2 to t3 corresponds to the secondperiod as a motion analysis target.

In addition, in this experimental example, as shown in FIG. 8, theposition of the sensor unit 10 at a time when the top 302 of the tennisracket 300 is at a maximum speed (immediately before the face of thetennis racket 300 is hit by the tennis ball 400) is set as the originpoint, the direction of the maximum speed of the top 302 is set to the Xaxis, and the Y axis and the Z axis are determined based on theright-hand system. Then, the trajectories of the top 302 and the gripend 304 of the tennis racket 300 in the XYZ coordinate system for thesecond period (the period of time t2 to t3) are displayed as graphs.

FIG. 9 is a flowchart of the process after the processing unit 200starts to acquire the output data of the sensor unit 10 until thetrajectories of the top 302 and the grip end 304 of the tennis racket300 for the second period in the XYZ coordinate system are displayed asgraphs.

First, until the data acquisition period ends (No in Step S120), newthree-axis acceleration data and three-axis angular velocity data areperiodically acquired from the sensor unit 10 (Step S110).

Next, when the data acquisition period ends (Yes in Step S120), an errorwith respect to the real value (0) of the three-axis angular velocitydata acquired in two first periods (the period of time t0 to t1 and theperiod of time t4 to t5) in Step S110 is calculated, and the timefunction of the output error (an error in the angular velocity) of thethree axis gyro sensors is estimated (Step S130). For example, the timefunction of the angular velocity error may be estimated throughapproximation as a polynomial equation.

Next, by using the time function estimated in Step S130, integration isperformed with the error of the three axis angular velocity dataacquired in Step S110 being eliminated, and the posture of the sensorunit 10 in the XYZ coordinate system is calculated (Step S140).

Next, by using the posture of the sensor unit 10 in the XYZ coordinatesystem that is calculated in Step S140, coordinate conversion of thethree axis acceleration data (an acceleration vector in the xyzcoordinate system) acquired in Step S110 into the acceleration vector inthe XYZ coordinate system is performed (Step S150).

Next, the acceleration vector in the XYZ coordinate system that isacquired through the coordinate conversion of Step S150 isdouble-integrated, and the positions of the sensor unit 10 in the XYZcoordinate system for the data acquisition period (the period of time t0to t5) are calculated (Step S160).

Next, the error with respect to the real value (the first position) ofthe position of the sensor unit 10 in the XYZ coordinate system for thetwo first periods (the period of time t0 to t1 and the period of time t4to t5) is calculated, and the time function of the acceleration error ineach direction of the X-axis, the Y-axis, and the Z-axis of theacceleration vector in the XYZ coordinate system is estimated (StepS170).

Next, by using the time function of the acceleration error that isestimated in Step S170, double integration is performed with the errorof the acceleration vector in the XYZ coordinate system beingeliminated, and the position (the position of the grip end 304 of thetennis racket 300) of the sensor unit 10 in the XYZ coordinate system iscalculated (Step S180).

Next, the distance and the direction from the sensor unit 10 to the topare measured in advance and are known, and the position of the top 302of the tennis racket 300 in the XYZ coordinate system is calculatedbased on the position of the sensor unit 10 in the XYZ coordinate systemthat is calculated in Step S160 and the posture of the sensor unit 10 inthe XYZ coordinate system that is calculated in Step S140 (Step S190).

Finally, the coordinates of the positions of the top 302 and the gripend 304 of the tennis racket 300 in the XYZ coordinate system for thesecond period (the period of time t2 to t3) as a motion analysis targetare extracted and are displayed as graphs (Step S200).

FIGS. 10A and 10B are diagrams showing an example of the trajectories ofthe top 302 and the grip end 304 of the tennis racket 300 for the secondperiod (the period of time t2 to t3). FIG. 10A illustrates thetrajectories in the X-Y plane, and FIG. 108 illustrates the trajectoriesin the X-Z plane. In FIG. 10A, a curve denoted by L1 is the trajectoryof the top 302, and a curve denoted by L2 is the trajectory of the gripend 304. In addition, in FIG. 10B, a curve denoted by L3 is thetrajectory of the top 302, and a curve denoted by L4 is the trajectoryof the grip end 304. The trajectories shown in FIGS. 10A and 10B areappropriate for the trajectory of an actual swing.

For a comparison, FIGS. 11A and 11B are diagrams acquired by displayingthe trajectories in an overlapping manner in a case where a generaltechnique of integrating without correction of the error of the threeaxis acceleration data in the trajectories shown in FIGS. 10A and 108.In FIG. 11A, a trajectory graph G1 is a graph (a trajectory graph in theXY plane in a case where the technique of this embodiment is applied) ofthe trajectory shown in FIG. 10A, and a trajectory graph G2 is a graphof the trajectory in the XY plane in a case where a general technique isapplied. In addition, in FIG. 118, a trajectory graph G3 is a graph (atrajectory graph in the XZ plane in a case where the technique of thisembodiment is applied) of the trajectory shown in FIG. 10B, and atrajectory graph G4 is a graph of the trajectory in the XZ plane in acase where a general technique is applied. Based on FIGS. 11A and 113,in the trajectory graphs G2 and G4 in a case where a general techniqueis applied, there is a displacement of 4 m in the X-axis direction, andit is apparent that the trajectory does not match an actual swingtrajectory. Based on this result, it can be understood that, by applyingthe technique of this embodiment, the accuracy of the swing trajectoryis improved to a large extent.

The invention is not limited to this embodiment, and variousmodifications can be made therein within the scope of the concept of theinvention.

For example, in this embodiment, a case has been described as an examplein which position data that is acquired by performing double timeintegration of the acceleration data is corrected. However, as anotherexample, speed data acquired by performing time integration of theacceleration data once may be corrected. In such a case, for example, ina case where the first period is set as a period in which the targetobject is stopped, the speed is zero for the first period, and the timefunction of the acceleration error can be estimated. By correcting thespeed as above, for example, the swing speed of a tennis racket, a golfclub, a bat, or the like can be measured with high accuracy. As anotherexample, data of an angle (rotation angle) of one axis rotation that isacquired by performing time integration of the angular velocity outputby the gyro sensor once may be corrected. In such a case, for example,in a case where the first period is a period in which the target objectis stopped, the rotation angle for the first period is set to zero, andthe time function of the acceleration error can be estimated. Bycorrecting the rotation angle as above, for example, the rotation angleof the hit area immediately after a tennis racket, a golf club, or thelike is hit by a ball (immediately after an impact) can be measured withhigh accuracy.

The invention includes a configuration (for example, a configurationthat has the same function, the same method, and the same result or aconfiguration that has the same object and the same effects) that issubstantially the same as the configuration described in the embodiment.In addition, the invention includes a configuration acquired bysubstituting a non-essential part of the configuration described in theembodiment. Furthermore, the invention includes a configuration thatexhibits the same operations and effects as those of the configurationdescribed in the embodiment or a configuration that can achieve the sameobject as that of the embodiment. In addition, the invention includes aconfiguration acquired by adding known techniques to the configurationdescribed in the embodiment.

The entire disclosure of Japanese Patent Application No. 2010-259234,filed Nov. 19, 2010 is expressly incorporated by reference herein.

What is claimed is:
 1. A motion analyzing apparatus comprising: a sensorunit that is installed to a target object and detects a physical amount;a data acquisition unit that acquires output data of the sensor unit ina period including a first period for which a real value of a value of mtime integrals (here, m is an integer equal to or greater than one) ofthe physical amount is known and a second period that is a target formotion analysis; an error time function estimating unit that performs mtime integrals of the output data and estimates a time function of anerror of a value of the physical amount detected by the sensor unit withrespect to the real value based on a difference between a value of mtime integrals of the output data and the real value for the firstperiod; a data correcting unit that corrects a value of m time integralsof the output data for the second period based on an estimation resultof the error time function estimating unit; and a motion analysisinformation generating unit that generates motion analysis informationof the target object based on the value of the m time integrals for thesecond period that is corrected by the data correcting unit.
 2. Themotion analyzing apparatus according to claim 1, wherein the error timefunction estimating unit estimates the time function of the error byapproximating the time function of the error as a polynomial equationand calculating coefficients of the polynomial equation.
 3. The motionanalyzing apparatus according to claim 1, wherein a plurality of thefirst periods is set, and wherein the error time function estimatingunit estimates the time function of the error based on data for each ofthe plurality of the first periods that is acquired by the dataacquiring unit.
 4. The motion analyzing apparatus according to claim 3,wherein at least one of the plurality of the first periods is a periodbefore start of the second period, and wherein at least one of theplurality of the first periods is a period after end of the secondperiod.
 5. The motion analyzing apparatus according to claim 1, whereinthe first period is a period in which the target object is stopped. 6.The motion analyzing apparatus according to claim 1, wherein the sensorunit detects at least one of acceleration and angular velocity as thephysical amount.